﻿Barus 
  — 
  Trial 
  of 
  Interferential 
  Induction 
  balance. 
  115 
  

  

  the 
  time 
  of 
  transmission 
  (g/2^o) 
  varies 
  as 
  z 
  already 
  given 
  

   and 
  proportionally 
  to 
  the 
  square 
  root 
  of 
  the 
  periodic 
  time. 
  

   Finally 
  the 
  magnitude 
  of 
  oscillation 
  decreases 
  in 
  geometric 
  

   progression 
  as 
  distance 
  increases 
  arithmetically. 
  

  

  In 
  case 
  of 
  a 
  circuit 
  made 
  and 
  broken 
  as 
  above, 
  the 
  quantity 
  

   which 
  may 
  be 
  called 
  the 
  retardation 
  a 
  (seconds) 
  has 
  the 
  value 
  

  

  a 
  = 
  '02332 
  CRx 
  % 
  lO" 
  6 
  

  

  where 
  C 
  is 
  the 
  capacity 
  in 
  microfarads 
  per 
  knot, 
  R 
  the 
  resist- 
  

   ance 
  in 
  ohms 
  per 
  knot, 
  x 
  the 
  length 
  of 
  cable 
  in 
  knots 
  (185,526 
  cm 
  ). 
  

   The 
  equation 
  would 
  not 
  be 
  changed 
  if 
  all 
  data 
  were 
  referred 
  

   to 
  the 
  centimeter. 
  The 
  current 
  reaches 
  50 
  per 
  cent 
  of 
  its 
  

   value 
  after 
  the 
  lapse 
  of 
  6a 
  seconds, 
  and 
  its 
  full 
  value 
  (nearly) 
  

   after 
  about 
  20a 
  seconds, 
  no 
  matter 
  what 
  cable 
  be 
  chosen. 
  

   Finally 
  the 
  capacity 
  of 
  the 
  cable 
  is 
  O 
  = 
  *0486 
  Kx/\og 
  D/d, 
  

   where 
  D/d 
  is 
  the 
  ratio 
  of 
  diameters 
  of 
  cable 
  envelope 
  and 
  

   cable 
  core, 
  K 
  (microfarads) 
  the 
  specific 
  inductive 
  capacity 
  of 
  

   the 
  substance 
  of 
  the 
  envelope. 
  

  

  To 
  test 
  the 
  speed 
  of 
  transmission 
  along 
  a 
  wire 
  with 
  resist- 
  

   ance 
  and 
  capacity 
  only, 
  let 
  the 
  wire 
  be 
  wrapped 
  bifilarly 
  and 
  

   the 
  capacity 
  of 
  the 
  bobbin 
  increased 
  by 
  surrounding 
  the 
  insula- 
  

   tion 
  of 
  the 
  wire 
  by 
  a 
  continuous 
  conductor. 
  I 
  will 
  suppose 
  

   this 
  to 
  be 
  done 
  with 
  silk-covered 
  wire 
  about 
  l 
  mm 
  in 
  diameter 
  

   with 
  sheets 
  of 
  tin 
  foil 
  around 
  the 
  successive 
  layers 
  to 
  increase 
  

   the 
  capacity. 
  Thus 
  if 
  D/d= 
  11 
  and 
  K= 
  2, 
  then 
  {7=2*5 
  

   microfarads. 
  Hence 
  the 
  retardation 
  per 
  knot, 
  if 
  the 
  resistance 
  

   per 
  knot 
  be 
  40 
  ohms, 
  is 
  a 
  = 
  2 
  3/10 
  6 
  , 
  and 
  the 
  current 
  would 
  

   attain 
  its 
  full 
  value 
  in 
  about 
  50 
  millionths 
  of 
  a 
  second, 
  for 
  the 
  

   first 
  knot 
  of 
  cable. 
  For 
  succeeding 
  knots 
  the 
  conditions 
  are 
  

   more 
  favorable. 
  

  

  It 
  follows, 
  therefore, 
  that 
  if 
  the 
  above 
  apparatus 
  is 
  to 
  

   measure 
  retardations 
  along 
  about 
  1*5 
  knot 
  of 
  the 
  wire 
  speci- 
  

   fied, 
  the 
  period 
  of 
  vibration 
  of 
  the 
  iron 
  cores 
  must 
  be 
  of 
  the 
  

   order 
  of 
  0*0001 
  second. 
  In 
  this 
  time 
  the 
  change 
  of 
  phase 
  

   would 
  be 
  complete 
  and 
  one 
  fringe 
  would 
  pass 
  the 
  cross-hairs. 
  

  

  The 
  point 
  finally 
  at 
  issue 
  is 
  whether 
  the 
  above 
  apparatus 
  can 
  

   respond 
  to 
  10,000 
  vibrations 
  per 
  second. 
  It 
  ought 
  not 
  to 
  be 
  

   difficult 
  to 
  break 
  the 
  current 
  as 
  often 
  as 
  this, 
  Gordon's* 
  rapid 
  

   speed 
  break 
  reaching 
  6000 
  per 
  second. 
  If 
  the 
  iron 
  cores 
  of 
  

   the 
  above 
  helices 
  be 
  clamped 
  in 
  the 
  middle 
  with 
  the 
  ends 
  free 
  

   to 
  vibrate 
  as 
  an 
  elastic 
  solid, 
  longitudinally, 
  a 
  length 
  slightly 
  

   over 
  30 
  cm 
  would 
  vibrate 
  with 
  the 
  given 
  frequency. 
  This 
  is 
  

   about 
  the 
  length 
  of 
  core 
  used 
  above. 
  

  

  On 
  the 
  other 
  hand, 
  it 
  is 
  necessary 
  to 
  wind 
  the 
  helices 
  for 
  

  

  * 
  Gordon 
  : 
  Electricity 
  and 
  Magnetism, 
  p. 
  49. 
  

  

  